Titel_SS06

Table 2.2: Concrete cube compressive strength experiment results in MPa.

The sample mean for the data set is readily evaluated using Equation (2.12) and found to be

equal to 32.67 MPa. All the observed values are different and therefore the mode cannot be

determined without dividing the observations into intervals as will be shown in Section 2.6.

However, the median is readily determined as being equal to 33.05 MPa.

Dispersion Measures

The variability or the dispersion of the data set is also an important characteristic of the data

set. This dispersion may be characterised by the sample variance s^2 given by:

2

1

1

(-)

n

i

i

sx

n 

  x^2 (2.13)

and the sample standard deviation is defined as the square root of the sample variance.

From Equation

s

(2.13) it is seen that the sample standard deviation s is assessed in terms of

the variability of the observations around the sample mean valuex.

The sample variance thus is the mean of the squared deviations from the sample mean and is

in this way analogous to the moment of inertia as used in e.g. structural engineering.

As a means of comparison of the dispersions of different data sets, the dimensionless sample

coefficient of variation  is convenient. The sample coefficient of variation  is defined as

the ratio of the sample standard deviation to the sample mean, i.e. given by:

s

x

 (2.14)

The sample variance for the concrete cube compressive strengths of Table 2.2 may be

evaluated using Equation (2.14) and is found to be 16.36 MPa^2. The sample standard

deviation is thus 4.04 MPa. For the considered concrete cube compressive strength data the

sample coefficient of variation is equal to 0.12. In the same manner the sample coefficient of

variation for the traffic flow data in Table 2.3 is equal to 0.21 and 0.30 for direction 1 and

direction 2 respectively. It is seen that the coefficient of variation for direction 2 is higher than

for direction 1. That indicates that the data observed in direction 2 are more dispersed than in

direction 1.